Pollock died at home Sunday from complications of cancer, the Las Vegas Review-Journal reported Tuesday.
In a statement, Burton said Pollock not only inspired him as a child, but became his mentor, teacher and "one of my closest friends."
"Channing was like a second dad to many," Copperfield said. "I am one of his 'sons.'"
Pollock started his career in 1952 and shot to stardom with an appearance on Ed Sullivan's "Toast of the Town" in 1954.
He appeared in several films as well, including "Europe by Night," "Musketeers of the Sea," "Rocambole" and "The Red Sheik." His many TV appearances included "The Beverly Hillbillies," "Bonanza," "The Hollywood Palace" and "The Andy Williams Show."
He is survived by his wife and a son. A Las Vegas memorial service was scheduled May 13 at the Monte Carlo.